倾斜层中的对流斑图及其临界条件

通过二维流体力学基本方程的数值模拟，探讨了Prandtl(普朗特)数Pr=6.99时，倾斜矩形腔体中的对流斑图和斑图转换的临界条件.根据倾角θ和相对Rayleigh(瑞利)数Ra_r的变化，倾斜矩形腔体中的对流斑图可以分为:单滚动圈对流斑图、充满腔体的多滚动圈对流斑图和过渡阶段的多滚动圈对流斑图.当θ一定时，随着Ra_r的减小，系统由充满腔体的多滚动圈对流斑图过渡到单滚动圈对流斑图.这时，对流振幅A和Nusselt(努塞尔)数Nu随着Ra_r的增加而增加.当Ra_r=9时，随着θ的增加，系统由充满腔体的多滚动圈对流斑图过渡到单滚动圈对流斑图，这时对流振幅A随着θ的增加而减小，Nusselt数Nu随着θ的增加而增加.在θ_c-Ra_r平面上对多滚动圈到单滚动圈对流斑图过渡的模拟结果表明， 在Ra_r=2时, 腔体中没有发现多滚动圈对流斑图.在Ra_r为2.5左右时，腔体中出现多滚动圈到单滚动圈对流斑图的过渡.当多滚动圈到单滚动圈对流斑图过渡的临界倾角θ_c<10°时，θ_{c随着Rar的减小而增加.当θc>10°时，θc随着Rar的增加而增加，在Rar≤5时，θc随着Rar的增加而迅速增加；当Rar>5时，θc随着Rar的增加而缓慢增加.θc与Rarθ的关系与Rar类似}     

水平来流对扰动成长和对流周期性的影响

对Pr=0.0272的纯流体在矩形腔体外加水平来流时,进行二维流体力学基本方程组的数值模拟.研究了该纯流体Rayleigh-Benard对流的一维行波斑图的成长及时空的演化.发现对流成长过程可以划分为3个阶段,即对流发展、对流指数成长和周期变化。在对流指数成长阶段对不同相对Rayleigh(瑞利)数Ra_r的最大垂直流速场随时间变化的情况进行分析,获得了最大垂直流速场指数成长阶段的线性成长率γ_m和相对Rayleigh数Ra_r的关系公式.研究了行波周期受水平来流Reynolds(雷诺)数的影响,揭示了行波对流周期性及其对水平来流Reynolds数的依赖性.     

侧向加热腔体中的多圈型对流斑图

基于流体力学方程组的数值模拟,研究了倾角θ=90°时侧向加热的大高宽比腔体中的对流斑图.对于Prandtl数Pr=6.99的流体,在相对Rayleigh数2≤Ra r≤25的范围内,腔体中发生的是单圈型对流斑图.对于Pr=0.0272的流体,取Ra r=13.9,随着计算时间的发展,腔体中由最初的单圈型对流斑图过渡到多圈型对流斑图,这是出现在侧向加热大高宽比腔体中的新型对流斑图.对不同Ra r情况的计算结果表明,Ra r对对流斑图的形成存在明显的影响.当Ra r≤4.4时是单圈型对流滚动;当Ra r=8.9~11.1时是过渡状态;当Ra r≥13.9时是多圈型对流滚动.对流最大振幅和Nusselt数Nu随着相对Rayleigh数的增加而增加.该对流斑图与Pr=6.99时对流斑图的比较说明,对流斑图的形成依赖于Prandtl数.     

具有水平流动的对流斑图成长和动力学特性

采用二维流体力学基本方程组对Prandtl数Pr=0.72具有水平流动的对流斑图成长和动力学特性进行了数值模拟.结果说明,对于给定的相对Rayleigh数Ra_r=5(Rayleigh数Ra=8 540)和Reynolds数Re=22.5,行波对流斑图的成长分为三个阶段,即对流发展阶段、指数成长阶段、周期变化阶段(过渡调整区、稳定周期变化区).行波对流的平均波数随着时间的发展或者对流斑图的成长而减小.随着相对Rayleigh数的增加,行波对流的指数成长阶段的时间变短,对流最大垂直流速的成长率变大.对于水平流动Re=5时,对流最大垂直流速的成长率γ_m与Ra_r的关系为γ_m=0.004 8Ra~(6.065 3)_r.在周期变化阶段,经过行波对流斑图和对流参数的过渡调整区后,对流进入斑图和对流参数的稳定周期变化区.对于给定的Ra_r=5时,行波对流的无量纲周期T_t随着Re变化的关系式为T_t=0.001 4Re~(2.363 5).     

底部形状对圆柱形港池中驻波的影响

本文用摄动法讨论了具有不规则底部的圆柱形港池中的驻波.假设流体是无粘性、不可压、无旋的.为方便起见,采用柱坐标系.速度势、波形以及频率均以相应于振幅的小参数进行摄动展开,获得了轴对称波驻的分析解,当ω₁=0时,算出了二阶频率.作为一个算例,取圆柱体底部为一轴对称抛物面,算出这种不规则底部对驻波产生灼影响.最后,对几何因素的影响进行了详细的讨论.     

趋旋性微生物在幂律流体饱和水平多孔层中的热-生物对流稳定性分析

基于趋旋性微生物和幂律流体模型,研究了在含有非Newton流体饱和多孔介质中生物对流的线性稳定性问题.利用Galerkin数值方法求解了该系统的控制方程,得到生物Rayleigh数的数值解,讨论了非Newton流体的幂律指数对生物对流稳定性在假塑性流体和膨胀性流体间的变化规律.研究结果表明,随着幂律流体的速度增大,幂律指数对生物对流稳定性的影响会发生变化,并且这种变化会受到热Rayleigh数和生物Lewis数的影响.另外,微生物趋旋性特征越明显,生物对流系统就越不稳定,而适当增大非Newton流体的幂律指数则有利于系统的稳定性.     

热泳和Brown运动对太阳能辐射下热分层纳米流体边界层流动的影响

在太阳辐射下的纳米流体中,数值地研究竖向延伸壁面具有可变流条件时的层流运动.使用的纳米流体模型为,在热分层中综合考虑了Brown运动和热泳的影响.应用一个特殊形式的Lie群变换,即缩放群变换,得到相应边值问题的对称群.对平移对称群得到一个精确解,对缩放对称群得到数值解.数值解依赖于Lewis数、Brown运动参数、热分层参数和热泳参数.得到结论:上述参数明显地影响着流场、温度和纳米粒子体积率的分布.显示出纳米流体提高了基流体热传导率和对流的热交换性能,基流体中的纳米粒子还具有改善液体辐射性能的作用,直接提高了太阳能集热器的吸热效率.     

多孔介质复合方腔双扩散混合对流LBM模拟

基于CLBGK模型,通过引入浓度分布函数,利用格子Boltzmann方法对顶盖驱动的复合方腔内的双扩散混合对流现象进行了研究,复合方腔由多孔介质区域和纯流体空间组成.在Richardson(理查德森)数Ri=1.0,Lewis(路易斯)数Le=2.0,Grashof(格拉晓夫)数Gr=104和Prandtl(普朗特)数Pr=0.7时,分析了孔隙尺度下多孔介质层不同位置及浮升力比（-5.0≤N≤5.0）对复合方腔双扩散混合对流的影响.给出了浮升力比N及多孔介质层位置影响下的高温高浓度壁面上的平均Nusselt(努赛尔)数Nu_av、平均Sherwood(舍伍德)数Sh_av及当地Nusselt数Nu_local和Sherwood数Sh_local的分布规律.     

具有非局部效应的时滞SEIR系统的周期行波解

该文研究了一类具有非局部效应和非线性发生率的时滞SEIR系统的周期行波解.首先,定义基本再生数R₀并构造适当的上下解,将周期行波解的存在性转化为闭凸集上非单调算子的不动点问题,利用Schauder不动点定理结合极限理论建立该系统周期行波解的存在性.其次,利用反证法结合比较原理,建立当基本再生数R₀<1时该系统周期行波解的不存在性.     

一类反应扩散系统的分歧与斑图

本文研究了一类发生在密闭容器中的不可激活的高次自催化反应扩散系统．在适当的条件下,用渐进近似的方法讨论了系统平衡态的稳定范围;用多重尺度的方法证明了当扩散系数λ充分小时,系统出现两种类型的斑图,一类是由Hopf分歧引出的驻波斑图;另一类是由 Pitchfork分歧引出的定波斑图．进一步还讨论了,在分歧点附近,对于大于空间或等于空间波数的小扰动,斑图是局部稳定的,而小于自身空间波数的小扰动,斑图是不稳定的．     

The Third-Harmonic Resonance for Capillary-Gravity Waves with O(2) Spatial Symmetry

It is well known that the addition of surface-tension effects to the classic Stokes model for water waves results in a countable infinity of values of the surface tension coefficient at which two traveling waves of differing wavelength travel at the same speed. In this paper the third-harmonic resonance (interaction of a one-crested wave with a three-crested wave) with O(2) spatial symmetry is considered. Nayfeh analyzed the third-harmonic resonance for traveling waves and found two classes of solutions. It is shown that there are in fact six classes of periodic solutions when the O(2) symmetry is acknowledged. The additional solutions are standing waves, mixed waves and secondary branches of “Z-waves.” The normal form and symmetry group for each of the solution classes are developed, and the coefficients in the normal form are formally computed using a perturbation method. The physical aspects of the most unusual class of waves (three-mode mixed waves) are illustrated by plotting the wave height as a function of x for discrete values of t.     

Solitary Roll Vortices in the Mixed Convection of a Vertical Fluid Layer

Some earlier experimental and numerical findings from convection in vertical channels suggest that localized convection rolls could play a role in the transition process of free or mixed convection. In the present work solitary convection roll vortices for a vertical fluid layer with stable stratification, differential shear and differentially heated side-walls have been obtained numerically for a fluid of unit Prandtl number. The solutions appear through saddle-node bifurcations and in certain parameter ranges they do also exist for linearly stable basic flow. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Localized Roll-Solutions in the Ekman-Couette-System

In the Ekman-Couette-System, where the usual Couette-System is additionally rotated about its normal axis, localized single roll solutions have been known for some time. By varying different system parameters, a new localized solution emerging by saddle-node bifurcations from these known solutions has now been found. This new solution is of the same localized nature like the old solution but with an additional roll. Further bifurcations lead then to an increasing number of rolls, still localized. This behavior is kind of analogous to the so called ‘homoclinic snaking’ which has recently been investigated in conjunction with the Swift-Hohenberg equation and binary fluid convection. It might link the unstable localized single roll solutions with stable multi roll solutions or even with stable periodic roll solutions, which has to be shown yet. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

TRAVELINGWAVE SOLUTIONS FOR A CLASS OF NONLINEAR DISPERSIVE EQUATIONS

The method of the phase plane is emploied to investigate the solitary and periodic traveling waves for a class of nonlinear dispersive partial differential equations. By using the bifurcation theory of dynamical systems to do qualitative analysis, all possible phase portraits in the parametric space for the traveling wave systems are obtained. It can be shown that the existence of a singular straight line in the traveling wave system is the reason why smooth solitary wave solutions converge to solitary cusp wave solution when parameters are varied. The different parameter conditions for the existence of solitary and periodic wave solutions of different kinds are rigorously determined.     

TRAVELING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR DISPERSIVE EQUATIONS

The method of the phase plane is emploied to investigate the solitary and periodic travelingwaves for a class of nonlinear dispersive partial differential equations.By using the bifurcationtheory of dynamical systems to do qualitative analysis,all possible phase portraits in theparametric space for the traveling wave systems are obtained.It can be shown that the existenceof a singular straight line in the traveling wave system is the reason why smooth solitary wavesolutions converge to solitary cusp wave solution when parameters are varied.The differentparameter conditions for the existence of solitary and periodic wave solutions of different kindsare rigorously determined.     

侧向局部加热对流的周期性

通过流体力学方程组的数值模拟,研究了侧向局部加热条件下Prandtl数Pr=0.0272时流体对流的周期性.结果表明:随着Grashof数Gr的增加,对流按稳态对流、单局部周期对流、双局部周期对流、准周期对流的顺序发展.当Gr<3.6×103时,对流为稳态;在3.6×103相似文献   

Wavelength selection in convection near a lateral boundary

^** Corresponding author. This paper considers the way in which a lateral boundary restrictsthe wavelength of convective rolls parallel to the boundary.Unlike previous theories of wave number selection, the presentwork allows for perpendicular cross rolls adjacent to the boundary,the existence of which is indicated by stability considerations.The present theory also incorporates forcing at the boundary,equivalent to a wall that is imperfectly insulated, as in manyexperimental investigations of Rayleigh–Bénardconvection. The results are based on weakly non-linear solutionsof amplitude equations derived from the Swift–Hohenbergmodel and are compared with numerical solutions of the fullnon-linear Swift–Hohenberg equation.     

Explicit Traveling Wave Solutions to Nonlinear Evolution Equations

First of all, some technical tools are developed. Then the author studies explicit traveling wave solutions to nonlinear dispersive wave equations, nonlinear dissipative dispersive wave equations, nonlinear convection equations, nonlinear reaction diffusion equations and nonlinear hyperbolic equations, respectively.